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Bases in Function Spaces, Sampling, Discrepancy, Numerical integration
EMS Tracts in Mathematics Vol. 11

Hans Triebel (University of Jena, Germany)

Bases in Function Spaces, Sampling, Discrepancy, Numerical integration

ISBN print 978-3-03719-085-2, ISBN online 978-3-03719-585-7
DOI 10.4171/085
June 2010, 305 pages, hardcover, 17 x 24 cm.
58.00 Euro

The first chapters of this book deal with Haar bases, Faber bases and some spline bases for function spaces in Euclidean n-space and n-cubes. This is used in the subsequent chapters to study sampling and numerical integration preferably in spaces with dominating mixed smoothness. The subject of the last chapter is the symbiotic relationship between numerical integration and discrepancy, measuring the deviation of sets of points from uniformity.

This book is addressed to graduate students and mathematicians having a working knowledge of basic elements of function spaces and approximation theory, and who are interested in the subtle interplay between function spaces, complexity theory and number theory (discrepancy).

Keywords: Function spaces, Haar bases, Faber bases, sampling, numerical integration, discrepancy

Further Information

Review in Zentralblatt MATH 1202.46002

Review in MR 2667814